Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity

We present a first complete implementation of an effective -one -body (EOB) model for extreme -massratio inspirals (EMRIs) that incorporates aligned spins (on both the primary and the secondary) as well as orbital eccentricity. The model extends TEOBResumS-Dali for these binaries by (i) recasting conservative first -order gravitational self -force (1GSF) information in the resummed EOB potentials, (ii) employing a post -Newtonian (PN) 3+19PN-accurate (3PN comparable -mass terms hybridized with test -particle terms up to 22PN relative order) expression for the gravitational -wave flux at infinity, and (iii) using an improved implementation of the horizon flux that better approximates its test -mass representation. With respect to our previous work [A. Albertini et al., Comparing second -order gravitational self -force and effective one body waveforms from inspiralling, quasicircular and nonspinning black hole binaries. II. The large -mass -ratio case, Phys. Rev. D 106, 084062 (2022).], we demonstrate that the inclusion of the 3+19PN-accurate l = 9 and l = 10 modes in the flux at infinity significantly improves the model's agreement with second -order accurate GSF (2GSF) circular waveforms. For a standard EMRI with mass ratio q equivalent to m1/m2 = 5 x 104 and m2 = 10M circle dot, the accumulated EOB/2GSF dephasing is less than or similar to rad for -1 yr of evolution, which is consistent with the standard accuracy requirements for EMRIs. We also showcase the generation of eccentric and spinning waveforms and discuss future extensions of our EOB towards a physically complete model for EMRIs.